The direct way to approach this question is to differentiate
Y with respect to L to get the marginal product of labor: |
dY/dL=MPL=(1-a)KaL-a. |
Now we want to know how this expression changes when
the capital stock increases. To find this, just differentiate again, this
time with respect to capital: |
d(MPL)/dK=d(dY/dL)/dK=d2Y/(dLdK)=a(1-a)Ka-1L-a>0 |
which is greater than zero because 0<a<1.
Thus, the marginal product of labor increases when capital increases.
This is equivalent to saying that the demand curve of labor shifting upward
at every possible quantity of labor when capital is increased (see the
answer to question 1). |